The distance correlation t-test of independence in high dimension
The distance correlation t-test of independence in high dimension
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DOI：
10.1016/j.jmva.2013.02.012
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发表时间：
2013-05-01
影响因子：
1.6
通讯作者：
Rizzo, Maria L.
中科院分区：
文献类型：
--
作者：
Szekely, Gabor J.;Rizzo, Maria L.
将距离相关推广到检验高维随机向量独立性的问题。距离相关性表征了独立性，并决定了任意维随机向量的多变量独立性检验。本文提出了一种修正的距离相关统计量，使得在独立的情况下，当维度趋于无穷大时，该统计量变换的分布收敛于学生t。由此，我们得到了任意高维随机向量独立性的距离相关t检验，它适用于保证某些极限定理有效性的坐标上的标准条件。这一新的检验是基于距离协方差的无偏估计，所得到的t检验对于大于三个或所有显著水平的样本大小是无偏的。在样本量大于9的情况下，变换后的统计量是近似正常的，提供了一个信息丰富的样本系数，很容易对高维数据进行解释。(C)2013 Elsevier Inc.保留所有权利。
Distance correlation is extended to the problem of testing the independence of random vectors in high dimension. Distance correlation characterizes independence and determines a test of multivariate independence for random vectors in arbitrary dimension. In this work, a modified distance correlation statistic is proposed, such that under independence the distribution of a transformation of the statistic converges to Student t, as dimension tends to infinity. Thus we obtain a distance correlation t-test for independence of random vectors in arbitrarily high dimension, applicable under standard conditions on the coordinates that ensure the validity of certain limit theorems. This new test is based on an unbiased estimator of distance covariance, and the resulting t-test is unbiased for every sample size greater than three and all significance levels. The transformed statistic is approximately normal under independence for sample size greater than nine, providing an informative sample coefficient that is easily interpretable for high dimensional data. (C) 2013 Elsevier Inc. All rights reserved.